Problem: Solve for $x$ and $y$ using substitution. ${3x-6y = 3}$ ${y = 6x+5}$
Explanation: Since $y$ has already been solved for, substitute $6x+5$ for $y$ in the first equation. ${3x - 6}{(6x+5)}{= 3}$ Simplify and solve for $x$ $3x-36x - 30 = 3$ $-33x-30 = 3$ $-33x-30{+30} = 3{+30}$ $-33x = 33$ $\dfrac{-33x}{{-33}} = \dfrac{33}{{-33}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = 6x+5}\thinspace$ to find $y$ ${y = 6}{(-1)}{ + 5}$ $y = -6 + 5$ $y = -1$ You can also plug ${x = -1}$ into $\thinspace {3x-6y = 3}\thinspace$ and get the same answer for $y$ : ${3}{(-1)}{ - 6y = 3}$ ${y = -1}$